Intro Question(s):
Count to 1000.
Get those soldiers across the river!
HW:
Go over law of cosines
Question: Baseball Diamond. From pitcher to home: 60.5 ft. Home to base: 90 ft. (it's a 90' square) Distance to first from mound?
Question: Baseball Player in Outfield. 300 feet to Home. Throws at 60 mph ... will the baseball player be able to make the throw all the way home? What's the farthest this person could throw? How long would it take?
Question: We showed the max distance a person can throw, and how long it takes to get there. But here's an extension. Say I have 2 players, each who can throw the ball at 60 mph. I want the ball to travel 400 feet as quickly as possible. In baseball, they often use a cut off person to achieve this (see video here). This is because they can often throw it faster this way -- more velocity in the x direction. Given this information, at what angle should each of the players throw to make the process as fast as possible. (in easy mode, assume the person in the middle takes no time to throw the ball again. For a more difficult question, assume it takes half a second for the person int he middle to catch the ball and then throw it again).
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Intro Question: Flashlight and Four People
Then: Trigonometry as a function.
the goal of this section is to make sure you can create an equation that goes around in a circle.
This can be achieved with sine or cosine fairly easily, as long as we follow the pieces we did in class.
here is your moment of zen. Sine is the height as we go around the circle, and cosine is the distance away from the center. They are the same thing, time shifted ninety degrees.
here is a link to the desmos I made for it.
change each of the variables and make sure you understand what's happening to it.
Question: Nantucket Average Temperature: https://www.desmos.com/calculator/gvagplqdtq
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Intro Question: To the moon.
The moon is 356,509 km away tonight.
If we take a piece of paper and fold it in half, then do so again, and again and again, how many folds are necessary to reach the moon?
So how can we make cool waves -- and why might we care?
Some interesting things for us to use when combining waves:
https://www.soundonsound.com/sos/apr08/articles/phasedemystified.htm
http://pages.uoregon.edu/emi/9.php
https://www.desmos.com/calculator/mvvamqk9xo
http://onlinetonegenerator.com/
I had mentioned a third reason to have these functions ...
Finally: Trigonometry as Trigonometric Identities
This should allow us to look at sin^2 + cos^2 = 1 .... and why that matters.
Let's combine some values and see what they look like in desmos. Try to quantify and possibly simplify some of these.
Looking at our sheet of information (from that super old book), let's see if we can add some facts we can use.